Killing plan ... Jeffrey Hall was shot by his son. Photo: Julie Platner/The New York Times

Because Joseph was so young at the time of the murder, the case hinged on whether he understood that shooting his father, Jeffrey Hall, 32, was wrong at the time. The judge, Jean Leonard, of Riverside County Superior Court in California, noted that after the shooting, Joseph put the gun under his bed, and did not cry when the police arrived, even as other family members were sobbing.

''These actions show the court that he knew his actions were wrong and did not want to get caught,'' Judge Leonard said in court on Monday. ''The killing was not spontaneous but planned.''

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The trial, which began in October but was delayed for months and only resumed last week, offered a rare and intimate glimpse into the life of a neo-Nazi's son.

Joseph had been violent most of his life, according to testimony, beginning before his father joined the National Socialist Movement. He hit his sisters and stepmother, stabbed classmates at school with pencils and once tried to strangle a teacher with a telephone cord.

As a result, he was expelled from at least half a dozen schools. ''He was very impulsive and very violent towards the other children and teachers,'' his stepmother, Krista McCary, testified during the trial. ''Hitting, kicking, biting, scratching, stabbing with sharp objects, hitting with objects.''

Hall also beat Joseph regularly years before the murder, the judge noted on Monday. The prosecutor, Michael Soccio, said he hoped the court would get Joseph help.